#364×C₇₁ #17985495

order	4544
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₇₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

#364×C₇₁

Subgroups

	subgroup	G/H
center	C₈×C₇₁	D₄
commutator	C₄	C₂×C₈×C₇₁
Frattini, cosocle	C₂×C₈	C₂²×C₇₁
socle	C₂×C₇₁	C₄⋊C₈
prime radical	C₂²×C₇₁	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₇₁ ◁ C₂×C₈×C₇₁ ◁ G

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 1136

A minimal faithful permutation representation — 2 generators on 87 points:

(1,2,5,10,6,9,14,16,7,11,13,8,4,15,3,12)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(1,3,4,13,7,14,6,5)(2,8,9,12,11,10,15,16)

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₁×#1335, C₇₁×#1336, C₇₁×#1357, …
maximal normal subgroup of	C₇₁×#1335, C₇₁×#1336, C₇₁×#1357, …
maximal quotient of	C₇₁×#1367, C₇₁×#1370, C₇₁×#1376, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 45);

#364×C71 #17985495